4 citations · 11 across the 10 of their papers we have counts for
10 papers
The first moment of primitive quartic \(L\)-functions with a secondary term
Ziwei Hong, Zhiyong Zheng
Let be a fixed odd prime power. We study the first moment of central values of primitive quartic Dirichlet -functions over $\F_q[T]$, with fixed genus and w…
The second moment of Ramanujan sums
Hong Ziwei, Zheng Zhiyong
In this paper, we study , the second moment of Ramanujan sums. Assuming the Riemann Hypothesis(RH), we establish an asymptotic formula for with improved error te…
An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem
Zhiyong Zheng, Fengxia Liu, Kun Tian
We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the dat…
On the High Dimensional RSA Algorithm -- A Public Key Cryptosystem Based on Lattice and Algebraic Number Theory
Zhiyong Zheng, Fengxia Liu
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few auth…
A Generalization of Cyclic Code and Applications to Public Key Cryptosystems
Zhiyong Zheng, Wenlin Huang, Jie Xu +1
In this paper, we define and discuss ϕ-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key en…
Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter
Zhiyong Zheng, Fengxia Liu, Yunfan Lu +1
Cyclic lattices and ideal lattices were introduced by Micciancio in \cite{D2}, Lyubashevsky and Micciancio in \cite{L1} respectively, which play an efficient role in Ajtai's constr…
Simultaneous Diophantine Approximation in Function Fields
Zhiyong Zheng
There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultan…
On the Polynomial Ramanujan Sums over Finite Fields
Zhiyong Zheng
The polynomial Ramanujan sum was first introduced by Carlitz [7], and a generalized version by Cohen [10]. In this paper, we study the arithmetical and analytic properties of these…
Davenport-Hasse's Theorem for Polynomial Gauss Sums over Finite Fields
Zheng Zhiyong
In this paper, we study the polynomial Gauss sums over finite fields, and present an analogue of Davenport-Hasse's theorem for the entire polynomial Gauss sums, which is a generali…
On the distribution of Jacobi sums
Qing Lu, Weizhe Zheng, Zhiyong Zheng
Let be a finite field of elements. For multiplicative characters of , we let denote the Jacobi sum. Nic…